Automatic Balancing of a Rigid Rotor with Misaligned Shaft

Abstract

We present a nonlinear analysis of the dynamics of an automatic ball balancer (ABB) for rotors which are both eccentric and misaligned. The ABB consists of two or more ball bearings which are free to travel around a circular race at a fixed distance from the shaft. The balls, after a transient response, find a steady state which balances the rotor. Following the previous work of Green et al. at Bristol, we have included the effect of shaft misalignment which causes the rotor to precess. This can be countered by having two ABB races at different axial locations along the shaft. Mathematically, we use a Lagrangian approach to derive the equations of motion for the system. It is found that, contrary to the case of flexible rotors that are subject to eccentricity and shaft bending, there is no choice of co-ordinate system which leads to autonomous governing equations. Simulations are then computed which illustrate the role of the ball damping coefficient.

Theoretical investigation into balancing high-speed flexible shafts, by the use of a novel compensating balancing sleeve

“…More recent work has considered on the possibility of 'automatic balancing', whereby weights have limited the movement to allow for balancing across a range of speeds. 11,12 This research was limited to a rigid rotor where the degree and position unbalance may change over time, and it remains difficult to achieve satisfactory results consistently over a large speed range for flexible shafts or rotors. Meanwhile, the use of controllable bearings, actuators and sensors to measure and control vibrations continues to be a work-in progress 13 due to the complexities surrounding the control system and the likely high cost of implementation.…”